Răspuns: Ai rezolvarea mai jos
Explicație pas cu pas:
Salutare!
[tex]\bf a)~ (3x+4)^{2} =100[/tex]
[tex]\bf (3x+4)^{2} =10^{2}[/tex]
[tex]\bf 3x+4 =\pm 10 \implies[/tex]
[tex]\bf 3x+4 =10 \implies 3x = 10-4\implies 3x = 6~~\bigg|:3 \implies\boxed{\bf x_{1} = 2}[/tex]
[tex]\bf 3x+4 =-10 \implies 3x = -10-4\implies 3x = -14 \implies\boxed{\bf x_{2} =-\dfrac{14}{3}}[/tex]
[tex]\it~~[/tex]
[tex]\bf b)~ (3x+1)^{2} =121[/tex]
[tex]\bf (3x+1)^{2} =11^{2}[/tex]
[tex]\bf 3x+1 =\pm 11\implies[/tex]
[tex]\bf 3x+1 = 11\implies 3x = 11-1\implies 3x = 10\implies \boxed{\bf x_{1}= \dfrac{10}{3}}[/tex]
[tex]\bf 3x+1 = -11\implies 3x = -11-1\implies 3x = -12\implies \boxed{\bf x_{2}=-4}[/tex]
[tex]\it~~[/tex]
[tex]\bf c)~ (4x+1)^{2} =225[/tex]
[tex]\bf (4x+1)^{2} =15^{2}[/tex]
[tex]\bf 4x+1 =\pm 15\implies[/tex]
[tex]\bf 4x+1 = 15\implies 4x = 15-1\implies 4x = 14\implies \boxed{\bf x_{1}= \dfrac{7}{2}}[/tex]
[tex]\bf 4x+1 = -15\implies 4x = -15-1\implies 4x = -16\implies \boxed{\bf x_{2}=-4}[/tex]
[tex]\it~~[/tex]
[tex]\bf d)~ (4-7x)^{2} =324[/tex]
[tex]\bf (4-7x)^{2} =18^{2}[/tex]
[tex]\bf 4-7x =\pm18 \implies[/tex]
[tex]\bf 4-7x = 18\implies -7x = 18-4\implies -7x = 14\implies \boxed{\bf x_{1}= -2}[/tex]
[tex]\bf 4-7x = -18\implies -7x = -18-4\implies -7x = -22\implies \boxed{\bf x_{2}= \dfrac{22}{7} }[/tex]
PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa
Bafta !
#copaceibrainly
